Centralizers in pseudo-finite groups

2017/02/27 by Hempel, Nadja, Palacin, Daniel
#FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.1702.08173

Abstract

The role of finite centralizers of involutions in pseudo-finite groups is analyzed. It is shown that a pseudo-finite group admitting a definable involutory automorphism fixing only finitely many elements is finite-by-abelian-by-finite. As a consequence, we give a model-theoretic proof of a result for periodic groups due to Hartley and Meixner. Furthermore, it is shown that any pseudo-finite group has an infinite abelian subgroup.

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